Henry and his new wife, meaghan, have disposable income of $192,000 per year. they can get a loan for 30 years at 3.5% apr. if they use this disposable income to purchase a home, what is the most expensive house they can afford?

They can afford a loan value of $1,781,560

Step-by-step explanation:

Generally, lenders like to see a family spend no more than 50% of their disposable income on debt service. If the home loan is the only debt Meaghan and Henry have, then they can afford a monthly payment of ...

... $192,000/12 × 50% = $8000

The loan amortization formula (or a calculator) can be used to find the corresponding loan principal amount, given the rate and time.

... A = P(r/n)/(1 -(1 +r/n)^(-nt)) . . . . for r=3.5%, n=12, t=30, A=8000

... $8000 = P(0.035/12)/(1 -(1 +.035/12)^(-12*30)) ≈ P(0.00449044688)

... P = $8000/0.00449044688) ≈ $1,781,559.88

This is the maximum amount Meaghan and Henry can finance, assuming no other debt. A typical home deal involves a down payment, and closing costs that may be over and above the price of the house. The most expensive house they can afford will depend on these other factors and the couple's ability to pay costs that are not financed (their savings or other sources of cash).